```python
def run_thermostat(start: int, low: int, high: int, power: int, drifts: list) -> dict:
    if not isinstance(start, int) or not isinstance(low, int) or not isinstance(high, int):
        raise ValueError("temperatures must be integers")
    if low >= high:
        raise ValueError("low must lie strictly below high")
    if isinstance(power, bool) or not isinstance(power, int) or power <= 0:
        raise ValueError("power must be a positive integer")
    if not isinstance(drifts, list):
        raise ValueError("drifts must be a list")
    for drift in drifts:
        if not isinstance(drift, int):
            raise ValueError("drifts must be integers")
    heated = False
    switches = 0
    coldest = start
    for tick in range(len(drifts)):
        current_temp = start + drifts[tick]
        if current_temp < low:
            heated = True
            switches += 1
        elif current_temp > high:
            heated = False
            switches += 1
        if current_temp < coldest:
            coldest = current_temp
    return {"temp": current_temp, "heated": heated, "switches": switches, "coldest": coldest}
```